Mplus Users Guide v6.. - Muthén & Muthén

CHAPTER 5computationally demanding as the number of factors and the sample sizeincrease. In this example, two dimensions of integration are used with atotal of 225 integration points. The ESTIMATOR option of theANALYSIS command can be used to select a different estimator. TheOUTPUT command is used to request additional output not included asthe default. The TECH1 option is used to request the arrays containingparameter specifications and starting values for all free parameters in themodel. The TECH8 option is used to request that the optimizationhistory in estimating the model be printed in the output. TECH8 isprinted to the screen during the computations as the default. TECH8screen printing is useful for determining how long the analysis takes. Anexplanation of the other commands can be found in Example 5.1.EXAMPLE 5.5: TWO-PARAMETER LOGISTIC ITEMRESPONSE THEORY (IRT) MODELTITLE: this is an example of a two-parameterlogistic item response theory (IRT) modelDATA: FILE IS ex5.5.dat;VARIABLE: NAMES ARE u1-u20;CATEGORICAL ARE u1-u20;ANALYSIS: ESTIMATOR = MLR;MODEL: f BY u1-u20*;f@1;OUTPUT: TECH1 TECH8;PLOT: TYPE = PLOT3;In this example, a logistic IRT model is estimated. With binary factorindicators, this is referred to as a two-parameter logistic model. Withordered categorical (ordinal) factor indicators, this is referred to asSamejima’s graded response model (Baker & Kim, 2004; du Toit, 2003).A single continuous factor is measured by 20 categorical factorindicators.The CATEGORICAL option is used to specify which dependentvariables are treated as binary or ordered categorical (ordinal) variablesin the model and its estimation. In the example above, the factorindicators u1 through u20 are binary or ordered categorical variables.The program determines the number of categories for each factorindicator. By specifying ESTIMATOR=MLR, a maximum likelihoodestimator with robust standard errors using a numerical integration60